Question

Darpana solved the equation s = a+b+c/3 for a. Her steps are shown below:

Answer 1

Answer:

The true statement is: In step 3 she needed to subtract c rather than divide.

Step-by-step explanation:

Lets solve our equation $s=\frac{a+b+c}{3}$ step by step.

Step 1. Since 3 is the denominator of the right hand side, we need to multiply both sides of the equation by 3:

$3s=\frac{3(a+b+c)}{3}$

Now we can cancel the 3 in the numerator and the 3 in the denominator to get

$3s=a+b+c$

As you can see, the first statement is false

Step 2. Since we want to isolate the variable $a$, we need to subtract b from both sides of the equation:

$3s=a+b+c$

$3s-b=a+b+c-b$

$3s-b=a+c$

The second statement is also false

Step 3. The last thing we to do to isolate $a$ (and solve for it) is subtract c from both sides of the equation:

$3s-b-c=a+c-c$

$3s-b-c=a$

$a=3s-b-c$

Therefore, the third statement is true: In step 3 she needed to subtract c rather than divide.

Answer 2

Answer: Third option (In step 3 she needed to subtract c rather than divide)

Step-by-step explanation:

When she subtract b from both sides of the equation, she obtained:

$3s-b=a+c$

Therefore, to leave the a alone at one member of the equation, she needs to subtract c from both sides of the equation.

Then, she would obtain the following:

$3s-b-c=a+c-c\\3s-b-c=a\\a=3s-b-c$

Therefore the answer is the third option: In step 3 she needed to subtract c rather than divide.